What is the sum from k=1 to infinity}((-1)^k*(1)^{(3*k) of)/k ?

The sum from k=1 to infinity}((-1)^k*(1)^{(3*k) of)/k is converges

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sum from k=1 to infinity}((-1)^k(1)^{(3k) of)/k

k = 1 \sum \infty \frac{( - 1 ) ^{k} \cdot ( 1 ) ^{(3 \cdot k)}}{k}

converges

Solution steps

k = 1 \sum \infty \frac{( - 1 ) ^{k} \cdot 1 ^{3 k}}{k}

Simplify

= k = 1 \sum \infty \frac{( - 1 ) ^{k}}{k}

Apply Alternating Series Test:

converges

= converges

What is the sum from k=1 to infinity}((-1)^k*(1)^{(3*k) of)/k ?
The sum from k=1 to infinity}((-1)^k*(1)^{(3*k) of)/k is converges